Final answer:
The given items are identified as an expression (56m - 7), equation (6b + 10 = 56), and inequalities (8n > 12, 78 < 2x - 3). An expression lacks equality or inequality symbols, while equations and inequalities make comparisons with equals, greater than, or less than signs.
Step-by-step explanation:
Identifying mathematical statements as expressions, equations, or inequalities is a fundamental skill in algebra. An expression is a combination of numbers, variables, and operators without an equality or inequality sign. An equation shows equality between two expressions, using an equals sign (=). An inequality compares expressions using inequality symbols such as <, >, ≤, or ≥.
- a) 56m - 7 is an expression as it does not contain an equality or inequality sign.
- b) 6b + 10 = 56 is an equation because it includes an equals sign, indicating that the two sides are equal.
- c) 8n > 12 is an inequality since it demonstrates that one side is greater than the other side using the > symbol.
- d) 78 < 2x - 3 is also an inequality as it shows that one side is less than the other side using the < symbol.
In the context of linear equations presented in the reference material, we see that they take the form y = mx + b, where m is the slope and b is the y-intercept. This equation expresses a linear relationship between two variables, usually with x being the independent variable and y the dependent variable.